English

The Nonlinear Stability of the Trivial Solution to the Maxwell-Born-Infeld System

Mathematical Physics 2015-05-19 v2 Analysis of PDEs math.MP

Abstract

In this article, we use an electromagnetic gauge-free framework to establish the existence of small-data global solutions to the Maxwell-Born-Infeld (MBI) system on the Minkowski space background in 1 + 3 dimensions. Because the nonlinearities in the system satisfy a version of the null condition, we are also able to show that these solutions decay at exactly the same rates as solutions to the linear Maxwell-Maxwell system. In addition, we show that on any Lorentzian manifold, the MBI system is hyperbolic in the interior of the field-strength regime in which its Lagrangian is real-valued.

Keywords

Cite

@article{arxiv.1008.5018,
  title  = {The Nonlinear Stability of the Trivial Solution to the Maxwell-Born-Infeld System},
  author = {Jared Speck},
  journal= {arXiv preprint arXiv:1008.5018},
  year   = {2015}
}

Comments

A few additional comments and some references were added. Some typos were corrected. 73 pages